User contributions for Robert Manc

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A user with 169 edits. Account created on 9 March 2023.
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5 December 2023

  • 15:5215:52, 5 December 2023 diff hist +49‎ 27024 ‎No edit summary
  • 15:2815:28, 5 December 2023 diff hist +993‎ N 27024 ‎ Pagină nouă: '''27024 (Gheorghe Szöllösy)''' ''Fie '' <math> I_n = \int_{0}^{\pi} \frac{\cos nx}{13-12\cos x}\,dx, n\ge0.</math>'' Să se calculeze '' <math>\lim_{n \to \infty}(I_0+I_1+I_2+\ldots+I_n).</math> '''Soluție. ''' ''Să observăm că'' <math>I_{n+2}+I_n = \int_{0}^{\pi}\frac{2\cos x-\cos(n_1)x}{13-12\cos x}\,dx = \frac{1}{6}\int_{0}^{\pi}\frac{(12\cos x-13+13)\cos(n+1)x}{13-12\cos x}\,dx= =\frac{1}{6(n+1)}\sin(n+1)x\Biggr|_{0}^{\pi}+\frac{13}{6}I_{n+1}, </math>'' oricare...
  • 15:1215:12, 5 December 2023 diff hist +84‎ Gazeta Matematică ‎No edit summary

28 April 2023

25 April 2023

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